Sunday, December 29, 2013

Savings and Income Scenario Settings

This is about the scenarios that can be generated and shown in the RIS software. I assume that you have dealt with the client settings and the market settings and have also set up one or more accounts and made at least one of them active. At this point you are almost ready to generate and plot scenarios, But you will probably first need to alter the initial scenario settings. The figure below shows the six settings and their default values in the RIS-20140101 version.

The first setting (line 2) indicates whether you want to project real (inflation-adjusted) or nominal values. I strongly suggest that you focus on real values for both savings and income, since these are far more relevant in estimating possible consumption of goods and services. However, it may be instructive in some cases to look at the nominal values, since some retirement income strategies focus on them. That said, it is important not to be fooled by such displays. For example, it is not enough for a strategy to provide constant or slightly increasing nominal income if the increases are not sufficient to cover inflation. Here is a simple bromide to keep in mind:

         Real people should care about real income

By all means, feel free to look at the nominal values of savings and income for scenarios, but then examine the real values in order to seriously evaluatie a strategy.

The second setting (line 4) indicates the number of future years that you wish to display on the savings and income graphs. Any values for subsequent years will be shown just outside the right-hand border of the graph. This conforms with a general rule: If a value falls outside the range of a graph, it is shown outside the border, using the closest x and/or y value

The remaining settings indicate the maximum values shown inside the borders for the four possible graphs (real savings, real income, nominal savings and nominal income). You may have to experiment a bit to find the most satisfactory values for these settings. A useful rule of thumb for strategies that rely on an initial investment is to set the maximum real savings at twice the initial investment and the maximum real income at twice the initial income. For nominal values it is useful to set maximum values at four times the initial amounts, since with typical settings for expected inflation, nominal values in the later years can be twice as large as real values.

I suggest that you use make rough estimates for all these settings, then generate some scenarios to see what happens. If too many values fall outside the borders, increase the corresponding setting. If there is too much empty space within the graph, decrease the corresponding setting. It should not take much time to find settings that provide a reasonable balance, excluding few values and using the space within the graph efficiently.

Once you have adjusted these scenario settings, you are ready to see the results of your handiwork by clicking either the savings scenario or income scenario button. I'll cover these in the next post.

Tuesday, December 17, 2013

The X% Rule


The RIS software allows the user to specify one or more sources of retirement income. Each is described in an account. And each such account has a number of settings.

An account might be a bank account, an account managed by a financial advisor, an annuity in which an insurance company provides monthly payments, etc.. All accounts provide annual payments that sum to equal retirement income. Many also have balances that sum to equal total savings. An account will make payments that may depend on the mortality of the recipients. Thus an account might pay more if both you and your partner are alive than if only one is alive. And in the first year in which you and your partner are both dead, any account with a balance will pay the total amount remaining to your estate.

In this post I will describe the first type of account, which I have called, generically, the X% Rule. This is a generalization of an approach widely recommended by financial advisors, based on a strategy initially termed the “4% Rule”.

The 4% rule

The 4% rule, first advocated by William Bengen in “Determining Withdrawal Rates Using Historical Data”, Journal of Financial Planning, vol. 7, no. 4, October 1994, pp. 171-180, is widely used by financial advisors. Bengen initially analyzed annual returns on bonds and stocks in the United States over every possible 30-year sub-period within  a 90-year period . For each sub-period, he calculated the outcomes of a policy of withdrawing a constant real amount equal to 4% of an initial investment value, assuming that funds were invested in a constant mix split evenly between stocks and bonds. He found that in almost all of the 30-year periods, such a policy would not “run out of money” and suggest that in this sense it “should be safe”. In a recent webinar he advocated following the policy with a withdrawal amount equal to 4.5% of the initial value.

Much has been written about the 4% rule. Jason Scott, John Watson and I analyzed it at considerable length in (“The 4% Rule: At What Price?”, Journal of Investment Management, vol. 7, no.3 (Third Quarter) 2009, pp. 1-18"), available here, in which we pointed out a number of its shortcomings. In a recent paper in the September/October issue of the Financial Analysts Journal,  Jason and John document subsequent studies of variants of the 4% rule and advocate a very different approach.

I won't go into details here, but my view is that the 4% rule and the variants that I have allowed in the x% account are sorely lacking. It seems to me that first principles dictate that any rule for spending out of a retirement account should at the very least adhere to the following principle:

        The amount you spend should depend on
              1. How much money you have, and
              2. How long you are likely to need it

    The x% rule can meet both criteria in the first year, since the amount spent is x% of the initial value and the value of x can be set taking into account the ages of the recipients (in practice, some advisors do modify the initial payment percentage, making it larger for older clients and smaller for younger ones). But after the first year, the rule fails on both counts. The amount paid is completely divorced from the value of the account. And no account is taken of changes in life expectancy, death of a principal, etc..

    In a quest for simplicity, the x% approach to providing retirement income comes up very short on first principles. However, since it persists as a kind of standard in much of the practice of financial advice, I have included it in the software. I'll have more to say about this in subsequent posts. In the meantime, I encourage you to experiment with different settings of the account, the market and the client to better understand the properties of this rule.

    Now to the details of the software.

    The X% account and its settings

    This section will cover details of the implementation of the account in the RIS software. I'll probably belabor some aspects that may be obvious. For many users it will suffice to look at the settings using the software, make any desired changes, and see the implications for savings and income in alternative possible future scenarios.

    The figures below shows the settings for the X% account. These may be reviewed and/or changed by clicking the "Account Settings" button on the RIS home page, then clicking the "X% Rule" button on the account settings page. When the settings have been reviewed or changed, simply press the keyboard left arrow to return to the home page.

    The initial setting (line 2) indicates whether this account is active or not. If an account type is not be be used, this setting must be N (no). When reviewing the settings for the account if the answer is N, the dialogue will be terminated and the account button will be dimmed. If the setting is Y the account button will be shown fully and the remaining settings will be reviewed and may be changed.

    The second setting (line 4) concerns the amount of money initially placed in the account. In general, dollar amounts in RIS are stated in thousands. In this default case the account starts with a million dollars (1000 $ thousand).

    The next setting (line 6) indicates the amount to be paid out initially, also stated in thousands of dollars. This will be paid immediately and is thus not subject to any uncertainty. In the default case this is equal to 40 ($ thousand), which is 4% of the initial investment, as in the classic 4% rule.

    The original formulation of the 4% rule did not take mortality into account. The assumption was made that an amount with the same purchasing power would be paid in each subsequent year unless there were insufficient funds, in which case the remaining funds would be paid out and subsequently nothing would be available

    In RIS I have generalized the approach somewhat to allow different amounts forthree possible conditions: both are alive (line 8), only you are alive (line 10) and only your partner is alive (line 12). In the default settings, all three equal the initial amount, giving the original 4% rule.

    The remaining settings concern fees and the investment strategy to be followed when implementing the rule.

    Line 14 shows the annual fee as a percentage of the account value. In the default case, 1% of the value of the account will be deducted for fees each year, just before payment is made to the beneficiaries. In practice a smaller fee (for example, 1/12 of 1%) is likely to be deducted each month but since RIS uses only annual returns and valuations, a single deduction is utilized. Financial institutions and advisors often charge lower percentage fees for larger accounts, but 1% is not atypical for accounts of a million dollars. You should adjust this setting to reflect the likely cost of such services in your case. Of course, you could follow an x% rule without an intermediary, saving a considerable amount of money. In such an instance you would set this amount to 0.

    The remaining settings describe the investment strategy to be followed. The original versions of the rule assumed that funds would be invested in a relatively constant mix of stocks and bonds – typically with 50 or 60% invested in stocks and the remainder in bonds. More recently, some have advocated the use of a “glide path” in which the proportions of bonds and stocks vary from year to year. To generalize, I have allowed for limited versions of either approach.

    To focus on real returns, RIS has only two major types of investments – a market portfolio and a riskless real security (as discussed in a previous post). Any investment strategy can thus described by the proportion of funds (by value) in the market. For example, if the proportion in the market is 0.60 (60%), the remainder (0.40 or 40%) will be invested in the riskless real security. The settings allow the proportion in the market to be as low as 0 and as high as 5. As I discussed in my earlier post, values greater than 1.0 assume that it is possible to “lever up” the market portfolio by borrowing at the riskless real rate of interest (or equivalently, that some sort of investment with the equivalent expected return and risk of such a levered position can be obtained) – an assumption that may be inappropriate in some cases.

    Three settings determine the investment policy. The first (line 16) indicates the initial proportion of funds in the market portfolio. This specifies the investment mix that will be used to determine the return at the end of the first year. In the default case it is 1.00, reflecting investment totally in the market portfolio. The next two settings determine the length of the “glide path” and the proportion invested in the market portfolio when it ends. For example, if the glide path were to last 20 years with the proportion in the market at that point equal to .50, line 18 would be set at 20 and line 20 at 0.50. The RIS software assumes that after the glide path ends, the proportion invested in the market remains constant. Thus if the glide path lasts 20 years and ends at 0.50, the proportion in the market portfolio will equal 0.50 in years 21, 22, and thereafter.

    The default settings specify the special case in which there is, in effect, no glide path. The market proportion starts at 1.0, the glide path lasts for 0 years and then the proportion continues at 1.0 thereafter.

    While the use of these three settings is somewhat forced in the default case, it seemed desirable to allow for a glide path in order to allow the analysis of approaches advocated by some practitioners. I have limited the possibilities by requiring the glide path to be linear, but this should capture at least the key attributes of approaches recommended by some analysts. A similar approach will be used for some of the additional types of account to be added to the software in the future.

    Once you have arranged the settings of an X% account to your satisfaction and made it active, you need only return to the RIS home page (via the keyboard left arrow) and click either the "Income Scenarios" or "Savings Scenarios" to see plots of possible future outcomes. It's that easy.

    Tuesday, December 3, 2013

    Investment Returns and Inflation

    With the exception of some social insurance programs, most sources of retirement income depend to a greater or lesser extent on the returns on one or more investment vehicles. The RIS software simulates returns on two types of such investments as well as changes in the overall cost of living.

    There are five key settings for this process, shown, along with default values, in the market settings list below.

    To see the current values of these settings and make any desired changes, simply click the Market Settings button on the RIS home page.

    This post will discuss the procedures used to provide simulated returns and changes in the cost of living as well as the reasons why I have chosen them for the initial releases of the software. I'll deal with the three key aspects in turn. 

    Warning! Of necessity, some of this discussion is going to be lengthy and rather technical. Feel free to skim it as needed.

    Risk-free real returns

    There are, at present, only two possible types of investment in the RIS software. The first is a risk-free instrument that promises a constant real return in each future year. An example of a (hopefully) risk-free real return instrument would be the Treasury Inflation-Protected Securities (TIPS) issued by the U.S. Government. The coupon and principal payments of such bonds are adjusted using a Consumer Price Index with the intention of providing fixed amounts of purchasing power. Of course the “cost of living” of any given individual or household will depend on the prices of a particular basket of goods and services and will, at best, only be approximated by a standard price index. There have been attempts in the U.S. To produce an index that more closely reflects the goods and services purchased by retirees, but the results were mixed and some concluded that the resulting index was not demonstrably superior to the standard CPI for this purpose.

    As you will see, in the scenario projections I have chosen to focus on real returns, real investment values and real retirement income since it is far more important to consider the spending power of future incomes than the nominal amounts. Unhappily, some vendors of retirement strategies market their products by focusing on seemingly desirable prospects for nominal income, leading retirees to fail to consider the erosion of purchasing power that inflation may cause. Many retirees will find that in the last years of their lives a dollar (or other currency) buys less than half the goods and services that it did when they retired. Those who ignore the possibility of inflation do so at their own great peril.

    As shown above, the default setting is for a real (inflation-adjusted) risk-free return of 1% per year in each future year. This “flat yield curve” assumption is at variance with both history and current yields on TIPS. For example, here are the TIPS real yields for bonds of various maturities at the end of November, 2013:

            Maturity         Annual Yield
                5 years           - 0.32 %
             10 years              0.60 %
             20 years              1.23 %
             30 years              1.53 %

    Such a “rising yield curve” is not uncommon. This may reflect a preference for more liquidity or possibly a prediction that shorter-term rates are likely to increase in the future. But it adds a complexity that is not currently included in the RIS software.

    Note also that at the time the real return on (relatively) riskless investments for a 5-year period was actually negative, suggesting that you could have invested your money for a promise to obtain fewer future goods and services than you sacrificed initially. To some extent this may have been due to a feature of TIPS that precludes reductions in payments below certain levels if there is deflation. But more likely it was an artifact of the “quantitative easing” program, in place at the time, in which the Federal Reserve Bank was purchasing huge amounts of government bonds each month in an attempt to hold interest rates down, due to the still tepid recovery from the recession of 2007-2009. Whatever the reason, low yields on both inflation-protected and traditional bonds imposes a huge burden on those attempting to finance their retirement – a result infrequently noted in the popular press and political discourse.

    In any event, the RIS system assumes that there is a constant riskless real rate of interest. The user is free to chose any desired value for this setting. The default of 1% is roughly equal to the average across all maturities in the latter part of 2013 and lower than the rates provided in previous years by inflation-protected securities in the U.S. and some other countries. While the lack of a complete term structure of interest rates in our simulations may omit important aspects of some possible investment policies, it may be an acceptable simplifying assumption for broad-based comparisons of alternative approaches.

    Market bond/stock portfolio returns

    The other possible type of investment in the RIS software is a portfolio of bonds and stocks. In the settings I call this the “market bond/stock portfolio” although I often refer to it simply as the “market portfolio”. Ideally, this should include all bonds and stocks traded relatively actively around the globe, with each represented in proportion to its outstanding value. In practice you may want to favor bonds from your home country.

    A key assumption is that the market portfolio includes securities with values proportional to the total outstanding values. Thus if the total outstanding value of Apple shares is $A and the total outstanding value of Microsoft shares is $M, the relative values of the two shares in the market portfolio will be $A/$M. More simply put, if the portfolio has x% of the total shares issued by Apple, it will have x% of the total shares issued by Microsoft and every other issuer. It will also have x% of the bonds issued by each of the included firms or governments. Importantly, changes in the relative prices of Apple and Microsoft will not require the purchase or sale of either. Actual trades will be required only to deal with dividends on stocks, coupon payments on bonds, share repurchases, bonds that are redeemed, new issues and the like. In this sense our market portfolio is a low-turnover fund and it should be possible to obtain an index fund with similar returns and low overall expenses.

    The market portfolio plays a central role in may theories of the pricing of capital assets and resultant prescriptions concerning the relative desirability of different investment strategies. Importantly, it represents the portfolio held by the sum of all those who invest in traded bonds and stocks. Any investor holding a different combination of such securities must, in a sense, be offset by one or more investors holding a complementary portfolio. Thus if I underweight Microsoft and overweight Apple relative to the market portfolio, one or more investors must overweight Microsoft and underweight Apple. Only the market portfolio can be said to be “macro-consistent” – that is, everyone could hold it and markets would clear.

    Note that our market portfolio is not the often-used market value weighted portfolio of equity securities, represented by some popular stock index. Rather it is intended to represent all relatively liquid bonds and stocks and therefore conform more closely to the “market portfolio” construct of academic theories about the pricing of capital assets.

    But how to predict the return on such a portfolio? Anyone with experience in security markets knows that it is impossible to predict the total return on the market in any given year. One can, at best, aspire to specify a range of possible outcomes and the likely probability of each one. Both academics and practitioners assume that this can be done, with the actual return considered a draw from a pre-specified probability distribution of possible returns. But what is the shape of the distribution? And what are its parameters: the central return, the range of possible returns, etc.?  It would be nice if we could reasonably assume that every year in history was a drawn from an unchanging probability distribution and if we had many centuries or such draws. But it is implausible that the return in 1865 was drawn from the same distribution as that in 2013. The world changes, the financial system varies, and the sources of uncertainty change as well. Despite decades of sophisticated statistical analyses, there is little agreement among academics and practitioners about "the" probability distribution of the return on the market portfolio.

    My opinion is that predicting the possible range of returns on the market is ultimately the responsibility of the investor with the aid of a financial advisor whom he or she trusts. I am not that advisor. The RIS software makes some assumptions about the type of probability distributions from which market returns and inflation will be drawn, but it is up to the user to choose the specific inputs. I have provided defaults that are similar to those used by some institutional investors, but you should feel free to change them. That said, the current software does employ a particular type of probability distribution and has additional built-in assumptions. If you believe these are not appropriate, you or someone else may  create a version of the software with different computations. The code is available at the Scratch site and you are free to make any desired modifications.

    In the current version of the software I have assumed that each year's total market return is drawn from a lognormal probability distribution. By “total market return” I mean the ratio of the year-end value to the value at the beginning of the year. Thus if the return is 10%, the total return is 1.10. Equivalently, I assume that the logarithm of the total market return is drawn from a normal distribution (the bell-shaped symmetric version that you undoubtedly studied in school). 

    Why this assumption? Here is a possible justification. The annual total return on a portfolio will equal the product of the daily total returns. From this it follows that the logarithm of the annual total return will equal the sum of the logarithms of the daily total returns. Now, as you may have learned in class, if you repeatedly add up a set of values each of which is drawn randomly from a distribution, the distribution of the sums will be close to a normal distribution, and the more the numbers you sum each time, the closer this will be to such a distribution (this is the famous “central limit theorem”). So if you think about the total return on the market over a year as the product of the total returns for each of the trading days in the year and assume that the daily returns are drawn independently, you will conclude that the distribution of annual total returns will be very close to lognormal. Moreover, the central limit theorem holds approximately in many cases where these assumptions are not met in every detail. In any event, such relationships can provide some justification for the assumption that annual returns are lognormally distributed. But there may be occasional "perfect storms" and the software does not take such a possibility into account; that said, the long run effects on retirement income for at least some strategies may not be radically different from those produced in the simulations.

    For good or ill, the RIS software draws each annual market return from an unchanging lognormal probability distribution. You (or I at some future date) could of course create a version with a different set of assumptions to accommodate, for example, a “fat left tailed” distribution or some other set of assumptions, but the current version doesn't allow for such an alternative.

    Two settings are used to fix the parameters of the market return distribution. The first is the expected annual return premium over the riskless real rate. For example, given the default value of 4% per year along with the riskless real return of 1% , the expected real return of the market portfolio would equal 5% (the sum). Note that this is the expected return, defined as the value obtained by weighting each possible value by its probability. The corresponding risk measure is the standard deviation of the annual real return, obtained by squaring the deviation of each possible real return from the expected value, weighting each such value by its probability, then taking the square root of the resulting sum. The default value is 12% per year. Note that, following convention, both these measures relate to the annual return, not its logarithm.

    An important relationship is given by the ratio of the market expected return premium to its standard deviation -- usually called the Sharpe Ratio (although I originally termed it the Reward to Variability Ratio). In this case it is 4/12, or 1/3. This is a commonly made assumption, reflecting a plausible relationship between risk and the additional expected return required for investors to bear the risk of a market portfolio.

    In traditional models of asset pricing such as the Capital Asset Pricing Model, the market portfolio provides the highest possible Sharpe Ratio. Combinations of the market portfolio and the riskless asset will provide the same Sharpe Ratio, assuming that investors can borrow or lend at the riskless rate. In the RIS software, all asset mixes are combinations of the riskless asset and the market portfolio, so this condition is met. However, substantial amounts of borrowing (negative positions in the riskless asset) at the same riskless rate may not in fact be feasible in the real world. Fortunately, most retirement income strategies involve investment risks equal to or lower than that of our market portfolio.

    In more general models of asset pricing such as those employing pricing kernels, the market portfolio also plays a central role. I have written about this in a 2007 book and utilized the approach in papers analyzing alternative retirement income strategies. For more information, see my web site.

    It is important to note that when total returns are lognormally distributed, the median (50/50) return will be smaller than the expected return, since the distribution of total returns will be skewed to the right. This is an important aspect of the RIS assumption. My view is that the expected return is a non-intuitive concept and that ordinary human beings relate far better to the median -- that is, the outcome for which there is roughly a 50% chance that the actual return will larger and a 50% chance that the return will be smaller. The distinction between the expected value  and the median is important when returns are drawn from asymmetric distributions, as they are in the software.

    A final assumption about market returns concerns the relationship between the return on the market in one year and that in the next. The software assumes that each annual return is drawn independently from a given lognormal distribution, so that there is no predictable relationship between one year's return and that of any other. In academic-speak, annual returns are independent and identically distributed (iid). An interesting aspect of such returns is that, regardless of the nature of the distribution of annual returns, the distribution of possible cumulative return over a period of many years will be close to lognormal, and hence skewed to the right (due to the the central limit theorem). In our case, however, the return over any period of years (from 1 to many) will be lognormally distributed.

    You may well wonder why only two possible investments are included explicitly in the RIS software. The reason is that in a simple setting, all efficient investment strategies should be constructed using the most efficient risky portfolio and a riskless security. We assume that people care about real, not nominal, returns and so the market portfolio is assumed to be the most efficient risky portfolio in real terms. Accordingly, the only real risk that is rewarded with greater expected real returns is the risk borne by investing in the market portfolio; moreover, this will be the case for any single year or multi-year holding period. No additional source of risk is rewarded with higher expected real returns.

    In the real world, many investment strategies recommended for retirees employ mixes of stocks and bonds. An investment in our market portfolio could be considered as roughly equal to a portfolio with 60% of its value in stocks and 40% in bonds. However, the relative values of stocks and bonds in our market portfolio will change as the relative values of outstanding stocks and bonds vary. The investor holding our market portfolio will not have to sell bonds and buy stocks when the stock market falls more than the bond market. Nor will he or she have to sell stocks and buy bonds when the stock market rises more than the bond market. As I have discussed elsewhere, strategies that call for specified proportions of value invested in stocks and bonds require “contrarian” behavior – selling relative winner and buying relative losers, and only a minority of investors can do this. As always, for every seller there must be a buyer. This calls into serious question the desirability of any investment strategy that requires rebalancing to maintain specific proportions of values of different asset classes, especially when trading costs are considered.

    My paper on these issues and a helpful calculator with historic data on the relative values of world bonds and stocks can be found here.

    Unfortunately, at present there is no low-cost mutual fund or ETF that provides returns similar to those of a world bond/stock portfolio. It is possible to find low-cost index funds or ETFs that cover the major components -- world stocks, U.S. Bonds and non-U.S. Bonds. But the investor holding such funds would have to monitor the relative values of these components periodically to adjust for new issues, bond maturities and the like. While this might not be too arduous, I continue to hope that the financial industry will  provide a single fund for those who wish to invest in a truly representative world bond/stock portfolio. In the meantime, relatively low-turnover mixes of broad-based bond and stock funds will probably suffice.

    If you wish to analyze strategies in which some alternative risky portfolio is utilized, you may of course adjust the assumptions about the market portfolio's expected return premium and standard deviation of return accordingly. However, any changes in asset allocation will have to rely on combinations of this portfolio and the riskless real security.

    A final issue in this area concerns our assumption that the expected return on the market is constant from year to year. Some evidence suggests that stock returns are not independently distributed from year to year. Instead, the stock expected returns may be higher after stocks have declined and lower after they have risen. Formally, the return on the stock market may have negative serial correlation. Importantly, this is not inconsistent with our assumption that the returns on the overall bond/stock market portfolio returns are independent from year to year. For example, assume that stocks have fallen in value and that the value of the stocks has changed from 60% of the total to 50%. If bond expected returns are unchanged, for the overall market expected return to be the same, stock returns will have to be greater. More generally, our assumption that the returns on the broad market of bonds and stocks are independent from year to year is not incconsistent with negative serial correlation in stock returns.


    The last two market settings relate to inflation. They are the expected annual inflation, for which the default value is 2.5% per year and the standard deviation of inflation, with a default value of 1.0%. While these are the parameters for annual inflation, the amounts generated for simulations are drawn from a lognormal distribution. Thus if annual inflation is 2.5%, the comparable relative value of purchasing power is 1.025 and in the simulations, the logarithms of such relative values are drawn from a normal distribution.

    For simplicity, the annual rates of inflation are assumed to be independently and identically distributed (in academic-speak, they are said to be iid). Moreover, they are assumed to be uncorrelated with the real returns on the market portfolio. These assumptions are somewhat inconsistent with much of the empirical evidence. Annual inflation appears to be positively serially correlated, with abnormally high periods of inflation likely to be followed by periods of smaller but still above-average values and with abnormally low periods of inflation likely to be followed by periods of higher but still below-average inflation. Moreover, in some countries there tends to be a negative relationship between real returns on equity and inflation, due perhaps to the fact that firms' taxes are based on nominal rather than real returns, so an increase in inflation may lower after-tax profits.

    While these empirical results raise relevant questions about our inflation assumptions, it is not likely that changing them would greatly affect the key simulation results. If the variation in inflation from year to year is relatively small, the impact on retirement income strategies may be minor. And, as is well known, central banks in most large countries and regions make every attempt to keep inflation within narrow ranges such as those assumed in our default settings. Our default assumption for the standard deviation of inflation (1%) may reflect an overly optimistic view of such banks' abilities to control inflation, but it can of course be easily changed.

    Turning to expected inflation, the target set by many if not most central banks is 2 % per year. Historically, many countries have experienced somewhat greater levels (and many advocate the central banks encourage this, at least when economies are sluggish). Some observers believe that expected inflation can be inferred from the spread between the yield on a nominal treasury security and that on a real security. For example, at the end of November, 2013 the real yield on a 20-year U.S. Treasury TIPS was 1.23% while the nominal yield on a regular U.S. Treasury bond with the same maturity was 3.54%. The difference (2.31%) could be a consensus of investors' estimates of future inflation over that period, although it might also reflect other considerations. In any event, our estimate of 2.5% may be reasonable, although it too can be easily changed.

    With simulated real returns on the market portfolio and inflation, it is easy to determine the associated nominal returns on the market. Rather than adding the two amounts I use the more precise relationship:
             (1+n) = (1+r)*(1+i)
    Thus if the market return is 8% and inflation is 2%:

            (1+n) = 1.08*1.02

    so (1+n) is 1.1016 and the nominal return is 10.16%. Given this relationship, the nominal returns on the market portfolio will be lognormally distributed, since both the market real return and inflation are lognormally distributed  and the product of two variables drawn from such distributions will be as well.


    Here are some key points concerning the market and inflation assumptions utilized in the RIS software.

    First, investors are assumed to diversify their risky asset holdings not only within asset classes but more broadly, across asset classes, focusing on a highly diversified portfolio of bonds and stocks. Second, the investment world is assumed to focus on real returns, with investors avoiding any “money illusion”. Third, the only risk that is rewarded with higher expected returns in any year or multi-year period is that associated with the broad overall market, represented ideally by the portfolio of all traded world bonds and stocks.

    The relative merits of different retirement income strategies may change if these assumptions are changed substantially, either by modifying the market settings or by changing the code to produce a system with qualitatively different investment and/or inflation assumptions. Outputs may well depend on inputs. My goal is to provide a base that others can use or modify as desired.

    Tuesday, November 19, 2013

    Video on Longevity

    Here is a video showing how to use the RIS system to obtain a longevity graph. It also provides an introduction to the general use of the software.

    The first few seconds may appear blurry, but don't give up -- the video will become clear very quickly.

    Monday, September 23, 2013

    Longevity Graphs

    There are many uncertainties associated with one's retirement years. This project is about retirement income – how much income will be available in each year and for how many years will income be needed. There will be much to say about the generation of income but a key aspect of any strategy for producing retirement income is the question of how long it will be needed.

    To put it crassly – how long will the primary recipients of income live?

    Very few want to address this question. But it is a key component of the process required to make sensible financial decisions in retirement. The programs that I will develop will rely heavily on longevity probability estimates. Hence it seems suitable to start the Retirement Income Scenarios (RIS) software with such estimates.

    Consider Bob and Sue Smith, whom we will call “The Client”. Bob is a 66 year old male and Sue a 63year old female. How long will they live? The answer is almost certainly that no one really knows. To approach this question in any rational manner one must deal with probabilities. Let's say that the probability that Bob will die next year is 1.3%. This means that out of cohort of 1,000 men of Bob's age, 13 are likely to die in the next twelve months. To put it more positively, 987 of them are likely to survive to reach 67.

    Mortality tables contain estimates of the probabilities of death at various ages for people in a particular segment of society. There are usually different tables for male and female members of that segment. Based on the numbers in the tables, estimates can be made of the probabilities that an individual or a pair of individuals will live to various ages. These are the probabilities shown in the RIS longevity graphs.

    For the RIS software I used tables provided by the United States Society of Actuaries based on statistics about the longevity of participants in a number of retirement plans in the U.S. The basic RP-2000 tables give estimated mortality probabilities for the year 2000 for (1) males and (2) females of various ages. The original data concerned mortality rates for employees up to age 70 and “healthy annuitants” (those receiving retirement benefits) from ages 50 through 120. Then these were combined to provide “combined healthy” mortality rates for all ages through 120 – the numbers that I used. For details, see the RP-2000 mortality tables.

    The Society of Actuaries has also produced two mortality improvement tables (BB) – one for males, the other for females. These provide estimates of the annual improvement in mortality for each age (although the annual improvements are zero for the lowest and highest ages). By applying these each year, it is possible to produce, in effect, a table for 2001, 2002, …, 2013, 2014 ,... and so on. The client settings in the RIS program include the current year to allow for updating to the present. Then the factors are used to compute estimates of future mortality. Thus Bob's mortality next year when he is 67 will be given by this year's mortality for a 67-year old plus the one year's mortality improvement using the factor for that age. The mortality for Bob the next year when he is 68, will be given by this year's mortality for a 68 year old male plus two times the annual mortality improvement factor for that age. And so on. For more on scale BB, see Mortality Improvement Scale BB.

    Of course, no one really knows the percentage of males or females of a given age that will die in each future year. There is thus uncertainty about the probabilities computed in this manner. I like to call this “table risk”. We don't really know what the future statistics will be. What if there is a cure for a major type of cancer? What if there is a nuclear holocaust? What if an antibiotic-resistant virus spreads around the world? The retirement income scenarios in my software will ignore this additional source of uncertainty. But insurance companies that sell annuities quite rightly worry about it a great deal, charging higher prices than would be dictated by standard annuity tables in order to provide a cushion if mortality rates increase (for life insurance) or decrease (for annuities). To some extent, this danger can be mitigated by issuing both types of policies, but life insurance is (appropriately) purchased mostly by younger people and annuities (appropriately) by older folks, so any offsets will be, at best, imperfect. I'll have more to say about the pricing of annuities and possible societal approaches for dealing with such table risk in later blogs.

    In practice there are many different mortality tables. Insurance companies use tables with higher mortalities when computing prices for life insurance policies, to reflect the likelihood that the pool of applicants will be less healthy than the average person (adverse selection) and that people with such policies might take more risk (moral hazard). Conversely, insurance companies use tables with lower mortalities for annuity policies, on the assumption that the pool of purchasers will be more healthy than the average person and likely to take better care of themselves.

    The U.S. Internal Revenue services requires corporate pension plans under its jurisdiction to use the RP-2000 tables with mortality improvement. A number of academic studies have utilized the tables as well. Hence my choice.

    Now, to the Longevity Graph feature of the RIS software.

    To access the current version of the software, go to and type wfsharpe in the search box. Then click on the latest RIS version shown. Click the green flag. You will see two buttons. Click the “Client Settings” button to see the current settings and to put in your own information. To leave a setting as is, simply press the Return key. When you are finished you will return to the main menu.

    At any time (except when you are entering inputs), you may press the keyboard up arrow to turn context-sensitive help on or off. You may also return to the main menu by pressing the keyboard left arrow.

    To make the software run faster at any time hold down the Shift key and click the green flag at the top of the window to place Scratch in turbo mode. To show the information in full-screen mode, click the icon at the top left of the window. To return to the smaller version, click it again.

    If you sign up for a free Scratch account, you may look at and, if desired, modify the software and save the revised version as a project in your own account at the Scratch site or on your own computer. If you have modified the client settings, the latest information will be saved with the software and will be available when you re-load it.

    So much for logistics – back to substance.

    If you feel that you or your partner are more or less healthy than the average healthy person of your age, you may want to put in a different age than your actual physical age. There are web sites that will give you an estimate for this purpose. I have looked at several and found them wanting. Some are blatant attempts to get your health information in order to sell you something (a magic elixir, anyone?). Others seem quite crude. I tried one that provides your “death date”. It took my health information, then told me that my death date had passed and parted by telling me to have a nice day (I'm not making this up). My friends confirmed that I am not yet dead (Monty Python fans will recognize the phrase). Perhaps the best approach is to ask your family doctor for his or her estimate of your effective age, health-wise.

    Once you have changed the client settings, click the “Longevity Graph” button and you will see your personal Longevity Graph. Here is the one for the Smiths:

    Each bar shows the probability that (1) both you and your partner will be alive in a future year, (2) only you will be alive in that year, or (3) only your partner will be alive.

    If you do not have a partner, change the client settings to make your fictional partner 120 years old. This rather crude approach will insure that he or she is not around in any future year.

    Of course in any specific projected future scenario you will live some specific number of years, as will your partner, This will be evident with alternative possible scenarios are shown in future versions of the RIS system. But the probabilities shown in the longevity graph provide some context as you think about alternative retirement income strategies.

    You may find all this terribly depressing. It is not pleasant to even think about dying and to consider the chances that you and/or your partner might not be around in some near or distant future year. On the other hand it may be depressing to think about the possibility that you will need income for decades in the future. I share your pain. But longevity is truly a fact of life, and it is one of three major uncertainties that must be faced when making plans for retirement income (the other two are investment returns and health issues). Forewarned is forearmed.

    Tuesday, September 17, 2013

    Why Scratch?

    As indicated in the previous blog, I am developing a suite of software dealing with retirement income scenarios using the Scratch programming language. Those who know something about Scratch may consider this a strange choice. Here I'll try to show why I consider it well suited for this project.

    I have been writing computer programs for over fifty years. My PhD dissertation included (in addition to an early version of the Capital Asset Pricing Model) the description of an algorithm for solving a special class of portfolio optimization problems and a program for implementing it. Since then I have written programs in a variety of languages. I published the first commercial book on the BASIC language and wrote an interpretive compiler to implement it when I was at the University of Washington. For my own research I now use Matlab, a scientific programming language. For years I used the standard Matlab constructs but now rely on the more recently added object-oriented capabilities. I love to program – there is much gratification when a program does what you intended it to do -- more than enough to offset the frustration when it doesn't.

    I also feel very strongly that everyone should be exposed to programming as part of the curriculum in Junior High School and/or High School. The benefits are many. Students can learn to think logically, divide complex tasks into a series of sub-tasks, test ideas rigorously, and explore aspects of mathematics, statistics and many other fields by doing experiments. They can also gain a deeper understanding of the ways in which computers, tablets, phones, televisions, movies and many things we encounter in our daily lives do what they do. Most people now spend hours every day interacting with technology but in an important sense they are interacting with programs. One hears “the computer did such and so” but it would be more accurate to say that a program made the computer do it.

    Most important, as the Scratch team emphasizes, one can experiment and be creative when writing programs – far more so than when using programs written by others.

    Unfortunately, programming is included in the required public curriculum in only a minority of public schools in most countries. There are groups trying to fill this need – see, for example,Computer Clubhouse, Coder Dojo, and But far more is needed.

    Since I had never taught pre-college students, I thought it would be a good idea to understand more about the benefits and challenges associated with including programming in the curriculum. I began by researching languages that would be suitable for doing so. I very shortly narrowed my list to one – the Scratch Programming Language developed at the Massachusetts Institute of Technology (MIT) (– for reasons that I'll give shortly. I spent some time learning the rudiments of the language and then volunteered to teach it to a small group of middle school students in a summer program sponsored by the Community Partnership for Youth in Seaside California, near my home in Carmel. I had a great time, as did the students. We wrote programs to create designs using geometric figures, to administer arithmetic tests, to run a horse race and to allow people to play pong. The students learned key aspects of logical thinking, how to break tasks into key components, and some applied mathematics. They also gained a better understanding of how much of the world of technology works. I learned as much from them as they did from me. Most importantly, it was great fun for us all.

    More than ever, I am convinced that the school curriculum needs to include programming. And that the best language, at least for the first course, is Scratch.

    Scratch was developed and is supported by the Lifetime Kindergarten research group at the MIT Media Lab. Work began in 2003 and the first version was launched publicly in 2007. At present there are over one million members of the Scratch Community and over three million projects have been posted on the Scratch web site.

    Here is a description of the choice of the name from a 2009 article by the members of the team ( Scratch: Programming for All).

    “The name 'Scratch' itself highlights the idea of tinkering, as it comes from the scratching technique used by hip-hop disc jockeys, who tinker with music by spinning vinyl records back and forth with their hands, mixing music clips together in creative ways. In Scratch Programming, the activity is similar, mixing graphics, animations, photos, music, and sound.”

    The most recent version, Scratch 2.0, became public in May, 2013. It allows users to write, edit and run programs using only a browser. Programs may also be downloaded to the user's computer. A downloadable version of the language editor and processor is also available (in a beta version as I write this).

    Anyone may join the Scratch community, create programs, and, if desired, make them available on the Scratch website. Any program made public by its author may be used by anyone. It is also possible to “look inside” to see a public program's code. Anyone may adapt such a program for other uses, subject only to the terms of a Creative Commons attribution and sharing license. As indicated earlier, users are encouraged to “remix” existing programs in order to create new capabilities (with attribution, of course) .

    There are no charges. The Lifetime Kindergarten group has received support from the likes of the National Science Foundation, the Intel and Microsoft Foundations, the MacArthur Foundation, Google and many others. Your support is also welcome but not required.

    It should not be surprising that an undertaking of this importance and quality comes from MIT. A legendary pioneer in the use of computers by people of all ages was Seymour Paper, who developed the Logo programming language. Indeed, Mitchel Resnick, the head of the Lifetime Kindergarten research group, recently published a description of the genesis of Scratch under the title Reviving Papert's Dream.

    This is not the place for a detailed description of Scratch. Resnik's recent paper is an excellent introduction, as is the formerly cited 2009 paper by the entire Scratch team. Here I'll give just a flavor of why it is different from most conventional programming languages.

    First, there are no error messages because it is very difficult, if not impossible to make a syntactic error. The grammar is based on a set of graphical programming blocks and items that are “snapped together” to create a program. And the items have shapes and colors that indicate their nature. If a something doesn't fit in a location, it can't be used in that manner. This avoids myriad errors, at the relatively small cost of requiring more grabbing, moving and assembling than required in most programming languages.

    Scratch has many attributes of a modern object-oriented programming language. Objects (called sprites) can have local variables and methods. Sprites communicate by broadcasting and receiving messages, which allows for more modular programming and event-driven execution. As indicated earlier, there are features that facilitate animation, graphic user input, graphic output, sound, inclusion of photos, external material and much more. If desired, programs can even be written to process input and output from some external devices.

    All these features make Scratch ideal for its intended purpose. The 2009 paper states: “The core audience on the site is between the ages of eight and 16 (peaking at 12), though a sizeable group of adults participates as well.” The students that I taught were between 11 and 13 and I can attest to the suitability of Scratch for that demographic. But next year I will be five times as old as the upper limit of the range for the core audience. Is Scratch right for me and for my work on retirement income? I think so.

    As I have learned more about Scratch and used it for complex projects, I have realized that the underlying structure is truly brilliant. The structure has been carefully crafted to allow great generality but with consistent and highly logical underpinnings. To be sure, there are limitations, but one can get around most of them or adapt as needed. At present I have not stressed the system by attempting very large simulations with sizable intermediate data, but early experiments indicate that Scratch can accomplish rather complex tasks quite efficiently.

    So, here is my plan. I will start with an overall structure that allows me to add features as items on a menu. The first release will have only one such feature (a “longevity graph”). Subsequent releases will add other features, all related in some manner to the forecasting and analysis of retirement income scenarios. I invite you to try the programs. Together we will see how far this undertaking can go.

    Monday, September 16, 2013

    Retirement Income Scenarios

    This blog will be devoted to discussions of issues surrounding the provision of income for a person or couple during their retirement years. Much of the analysis will be conducted by forecasting a number of possible future scenarios, then analyzing the properties of chosen strategies for producing retirement income across the scenarios. I call this approach “retirement income scenario analysis”. It uses the method of Monte Carlo simulation with an underlying set of assumptions about the behavior of capital market and macro-economic variables as well as an assumed basis for valuations of possible future cash flows.

    Since it is important to generate sufficient scenarios to provide a representative set of possible future outcomes, computer programs play a central role in the analyses. I have developed a series of routines for large-scale projections using the Matlab programming language, taking particular advantage of its object-oriented capabilities. I have been using Matlab for decades and find it an excellent language for scientific analysis. However, there is no simple way to make Matlab programs available for use by those who have not purchased the software or have access to it through colleges and universities. Hence I do not plan to try to make these programs available for use by others. Instead I will use the Matlab programs to illustrate and illuminate some of the fundamental relationships involved in retirement income planning.

    Fortunately, there is a programming language that can freely be used by anyone, and a supporting system that allows programs to be made available for use, study and modification by others. Moreover, only a standard web browser is required to use the system or to run programs written in the language. Its name? Scratch. I am in the process of preparing a series of programs written in Scratch that will be available for anyone to use, study or modify.

    I'll discuss Scratch and the reason why I chose it in some detail in the next blog. Subsequent blogs will describe the components and capabilities of the Scratch programs as I complete them and make them available. I call the overall system RIS, which stands for Retirement Income Scenarios. As befits the subject of a series of blogs, this is an ongoing undertaking, with capabilities that will grow over time.

    Of course there will be more in the blogs than discussions of programs. Much of the material will deal more generally with key aspects of the economics of retirement income..

    There is much to cover. Please join me in trying to understand and explore the many relevant aspects of this crucially important topic.

    Sunday, August 4, 2013

    Plans for this blog

    This is a new blog on which I plan to post material on creating and analyzing ranges of scenarios for retirement income using different strategies for investing, spending and annuitizing retirement savings.

    With luck, I'll have new material here relatively soon.